It was the second straight win for the Dodgers, owners of the best road record in baseball (38-25), owners of the best overall record in the National League (68-52), and owners of a five-game lead over the idle Giants in the National League West.
Correia retired the first nine batters he faced and through three innings outhit the Braves 1-0.
But in the fourth a leadoff single to center by Emilio Bonifacio ended any perfect game thoughts. A sacrifice bunt and a walk but Correia in a rough patch, and Justin Upton made him pay with a scorched single up the middle for a 1-0 Atlanta lead.
But Correia was able to limit the damage by striking out Jason Heyward and getting Evan Gattis to fly out to left to end the threat. That was the only fly out of the game against Correia, who induced 10 ground ball outs and lasted six innings, allowing just the one run on four hits.
Correia also struck out five, one off his season high and the most he has had in a game since May 26, 14 starts ago. In the 13 starts in between that start and Monday night, Correia struck out 30 of 325 batters faced, or 9.2 percent.
On Monday, Correia struck out 21.7 percent of his batters faced.
The Dodgers slowly and methodically rallied their way into a lead against Julio Teheran in the sixth, a rally started with Correia's second hit of the night.
It was the first multi-hit game of Correia's career, a .115/.147/.135 hitter. Correia is the second Dodgers pitcher in the last 14 years with two hits in his first game with the club, joining Ricky Nolasco (2013).
Dee Gordon followed with a single to right field, then Yasiel Puig smashed one hard to left, hit too hard for Correia to score from second base. That loaded the bases, a well-documented terrible situation for the Dodgers this season, hitting just .167/.198/.218 in 86 plate appearances entering Monday, worst in baseball across the board, along with a .220 batting average on balls in play (well below the major league .294 BABIP in bases loaded situations in 2014).
On Monday, the Dodgers' fortunes turned and their bases loaded cup runneth over.
Adrian Gonzalez singled to right field, a ball that appeared like it might be caught, so everyone advanced on base to tie the game at 1-1. After Matt Kemp popped out, Carl Crawford hit an infield single into the hole between first and second base, giving the Dodgers a 2-1 lead.
Justin Turner followed with an easy double play ball to the second baseman Bonifacio, but it was bobbled, meaning only one out at first base and another run scoring, giving the Dodgers a 3-1 advantage.
The Dodgers rallied again in the eighth inning, highlighted by a ground rule double by Kemp. After Crawford drove home an insurance run with his third single of the night, the club loaded the bases again.
This time it was A.J. Ellis who hit the potential double play ball to second base, but Turner had a great takeout slide causing shortstop Ramiro Pena to throw the ball away, allowing two more runs to score instead of ending the inning.
On the night the Dodgers were 2-for-6 with the bases loaded, and scored more runs on the would-be double play balls (three) than on the hits (two). Such is baseball.
Gonzalez was 2-for-5 on Monday, his fifth straight multi-hit game, matching Turner (June 6-12) for the longest streak by a Dodger this season.
Gonzalez also drove in his 80th run, his fifth straight game with an RBI. He has had separate RBI streaks this season of seven, five and five games.
Puig was 2-for-4 with two runs scored, hit ninth multi-hit game in 12 career games against the Braves, including the playoffs. Puig in his career is 25-for-49 (.510) against Atlanta, with at least one hit in every game.
Darwin Barney made his Dodgers debut in the top of the seventh, pinch hitting for Correia. Barney grounded out to third base.
Jason Heyward was 0-for-4 with two strikeouts. In 28 career games against the Dodgers, the outfielder is hitting .158/.259/.198 with just three extra-base hits, and no home runs. Against everyone else, Heyward is hitting .265/.356/.444.
Teheran picked off two Dodgers off first base, Crawford in the second and Puig in the fourth inning. Teheran, who led baseball with eight pickoffs in 2013 - one more than Clayton Kershaw - has four pickoffs on the season.
Pena entered the game at shortstop in the second inning when starting second baseman Tommy La Stella left with a cramp in his upper right hamstring. The Braves announced they expected La Stella to return to the lineup on Tuesday. Bonifacio, who stared at shortstop in place of an injured Andrelton Simmons, moved to second base.
The Dodgers are 8-4 on Mondays this season, but have the next two Mondays off.
The Dodgers rotation got an extra day of rest thanks to Correia on Monday, which means Dan Haren will be on five days rest in the second game of the series on Tuesday night. Mike Minor starts for the Braves, the only left-handed pitcher slated to face Los Angeles this week.
Home runs: none
WP - Kevin Correia (6-13): 6 IP, 4 hits, 1 run, 1 walk, 5 strikeouts
LP - Julio Teheran (10-9): 7⅓ IP, 9 hits, 5 runs, 2 walks, 6 strikeouts